Eur. Phys. J. Plus (2017) 132: 475
https://doi.org/10.1140/epjp/i2017-11752-9

Regular Article

Jacobi elliptic solutions, solitons and other solutions for the nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity

¹ Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, Egypt
² Department of Mathematics, Faculty of Education and Science, Taiz University, Taiz, Yemen

^* e-mail: alnowehy2010@yahoo.com

Received: 26 July 2017
Accepted: 12 October 2017
Published online: 13 November 2017

Abstract

Based on several integration tools, namely the Riccati equation method, the Bernoulli equation method, the extended auxiliary equation method, the new mapping method and the -model expansion method, we obtain many exact solutions including the optical bright-dark-singular soliton solutions, Jacobi elliptic solutions and trigonometric function solutions of the nonlinear Schrödinger equation (NLSE) with fourth-order dispersion and cubic-quintic nonlinearity, self-steeping and self-frequency shift effects which describes the propagation of an optical pulse in optical fibers. We compare the results yielding from these integration tools together with each others. Also, a comparison between our results in this paper and the well-known results are given.